Abstract:We define and study the higher rank GKZ-fans of point configurations, serving as the set of discrete and homogeneous quasi-valuations on the homogeneous coordinate ring of the associated toric variety, where the rank one cases coincide with the usual GKZ-fans. Such a quasi-valuation is then used to degenerate the toric variety flatly to a reduced union of toric varieties, which encodes the polytopal subdivision arising from the point in the higher rank GKZ-fan.
From: Xin Fang [view email]
[v1]
Wed, 22 Apr 2026 06:58:09 UTC (46 KB)
[v2]
Sun, 13 Sep 2026 19:38:04 UTC (34 KB)
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